# How to isolate Xc in this equation?

Discussion in 'Homework Help' started by Flupps, Jan 24, 2014.

1. ### Flupps Thread Starter New Member

Nov 14, 2013
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0
I'm stuck on a homework problem I have.

Q1: For the circuit in question1above: R=(5.80x10^2) (Ω) and C=(4.5000x10^-7) (F). At what frequency the lagging angle of the impedance θ=(3.400x10^1)°. Enter the answer in (Hz)

I believe I first need to isolate Xc in the below equation
θ = tan-1(Xc/R)

Once I figure out Xc I can use f = 1/(2*pi*Xc*C) to calculate the frequency

Could anyone please tell me how to isolate Xc in the first equation?

Thanks!

2. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,499
511
Ah. You are so close!

Ok. The key formula here is:
theta=tan^-1(-Xc/R)

Here is the thing, you are not interested in Xc, you are interested in one of the components that make up the Xc! Very important this point.

What is Xc? It is:
Xc= 1/(2*pi*f*C)
You want the f!

So. The earlier formula becomes:
theta=tan^-1[(-1/(2*pi*f*C))/R]
theta is given.
C is given.
R is given.
Solve for f.

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3. ### Flupps Thread Starter New Member

Nov 14, 2013
8
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ah I see, but I am not sure how to isolate f in that equation? I have always been confused about rearranging equations like this

4. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,499
511
Dude, you are making me sad.

tan(theta)=[-1/(2*pi*f*C)]/R

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5. ### Flupps Thread Starter New Member

Nov 14, 2013
8
0
ah my bad, I got it now tyvm